Method of estimating the parameters and state of power system of electric vehicle

ABSTRACT

A method for estimating parameters and the state of a power system of an electric vehicle is disclosed. A multi-time scale model of the power system is set up; a parameter observer AEKF θ  based on a macroscopic time scale and a state observer AEKF, based on a microcosmic time scale in the power system of the electric vehicle are initialized; time update is performed on the parameter observer AEKF θ , the updating time span is one macroscopic time scale, and a priori estimation value {circumflex over (θ)} −   l  at the moment t 1,0 , of the parameter θ is obtained; time update and measurement update are performed on the state observer AEKF x  and circulated for L times, so that the time of the state observer AEKF x  is updated to the moment t 0,1 ; and measurement update is performed on the parameter observer AEKF θ , and the operation is circulated until the estimation is finished. By means of the method, the parameters and the state of the power system of the electric vehicle are estimated, the precision is high, the calculation time is short, and calculation costs are reduced.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of International Patent ApplicationNo. PCT/CN20141078608 with a filing date of May 28, 2014. designatingthe United States, now pending, and further claims priority to ChinesePatent Application No. 201410225424.6 with a filing date of May 26,2014. The content of the aforementioned applications, including anyintervening amendments thereto, are incorporated herein by reference.

TECHNICAL FIELD

This invention is about system identification and state estimation,especially related to methods of parameter and state estimation of apower system made up of a drive motor and a battery used in electricvehicles, as well as an electric vehicle battery management system.

BACKGROUND OF THE PRESENT INVENTION

State-space is a general method to deal with the nonlinear controlsystem. When using the state-space to the nonlinear control system, thestate equation is applied to describe the dynamical characteristics ofthe nonlinear control system, and the observation equation is used todescribe the relationship of observations and states of nonlinearcontrol system. Based on which, the hidden states will be estimated inreal time by using the observed information involved noise. However, theuncertain parameters contained in the state equation and observationequation have negative influence and will result in the low estimationaccuracy of the hidden states of nonlinear control systems.

In order to solve this problem and improve the hidden states estimationaccuracy of the nonlinear control system, the technicians in this fieldoften identify the uncertain parameters of state equation andobservation equation by an experimental way. Then the hidden states ofnonlinear control system will be estimated based on the determinedstate-space equation.

For example, the technicians in the battery control field often obtainthe battery parameter by an experimental approach to construct thebattery model. Then, the battery state estimation and optimization ofthe electric vehicle energy management will be operated based on theconstructed battery model. Because the battery parameter set isinfluenced by the internal and external factors, such as battery agingand environmental change, which will lead to obvious change of thebattery parameter sets, stable and reliable state estimation will behard to obtain based on the previously constructed battery models.Furthermore, it is hard to obtain the convergent and optimal solution byusing the traditional Kalman filter approach, since the batteryparameter possesses the slow time-varying characteristics caused by theinternal and external factors while the battery state possesses the fasttime-varying characteristics influenced by the parameter change, whichwill result in the increase of calculation burden of the control system.

In conclusion, because the parameter of the nonlinear control systemwill change, it is hard to obtain the stable and reliable state estimatewhen applying the parameter identified by the experimental approach toestimate the nonlinear control system state. Besides, as a result of theslow time-varying characteristics of the system parameter set and fasttime-varying characteristics of the system state, the long calculationtime and high calculation burden will be caused by using the traditionalKalman filter for the state estimation of the nonlinear control system.

Also, the estimation error is within 5% with the commonly used batterymanagement system applied in electric vehicles for SoC estimation, andthe available capacity estimation error is within 10%,

SUMMARY OF PRESENT INVENTION

In order to get stable and reliable state estimation of the electricvehicle and reduce the calculation cost, this invention proposes amethod for estimating the parameters and the state of a power system ofan electric vehicle. The method comprises the following steps of:

Step 1, constructing a multi-time scale model of he power system

$\quad\left\{ {\begin{matrix}{{x_{k,{l + 1}} = {{F\left( {x_{k,l},\theta_{k},u_{k,l}} \right)} + \omega_{k,l}}},{\theta_{k + 1} = {\theta_{k} + \rho_{k}}}} \\{Y_{k,l} = {{G\left( {x_{k,l},\theta_{k},u_{k,l}} \right)} + v_{k,l}}}\end{matrix},} \right.$

in which

θ indicates the parameters of the power system,

x indicates a hidden state of the power system,

F (x_(k,l), θ_(k), u_(k,l)) indicates a state function of the multi-timescale model,

G(x_(k,l), θ_(k), u_(k,l)) indicates an observation function of hemulti-tune scale model,

x_(k,l) is the power system state at moment t_(k,l)=t_(k,0)+l×Δt(1≦l≦L),and k is the macroscopic time scale, l is the microscopic time scale, Lis the transfer threshold between the microscopic and macroscopic timescale.

u_(k,l) is the input information of the power system at a momentt_(k,l),

Y_(k,l) is the measurement matrix of the power system at a momentt_(k,l),

ω_(k,l) is the white noise of the power system state, its mean is zeroand its covariance is Q_(k,l) ^(x),

ρ_(k,l) is the white noise of the power system parameter, its mean iszero and its covariance is Q_(k) ^(θ),

ν_(k,l) is the measurement white noise of the power system, its mean iszero and its covariance is R_(k,l),

θ_(k)=θ_(0L−l),

Step 2, initializing θ₀, P₀ ^(θ), Q₀ ^(θ) and R₀ of the parameterobserver AEKF₀ based on the macroscopic time scale, in which

θ₀ is the parameter initial value of the parameter observer AEKF_(θ),

P_(θ) ^(θ) is the initial covariance error matrix value the parameterestimation of the parameter observer AEKF_(θ),

Q₀ ^(θ) is the initial covariance error matrix value of the power systemnoise of the parameter observer AEKF_(θ),

R₀ is the observation noise of the pare meter observer AEKF_(θ);

initializing x_(θ,θ), P_(θ,θ) ^(x), Q_(θ,θ) ^(x) and R_(θ,θ) of thestate observer AEKF, based on the microscopic time scale, in which,

x_(θ,θ) is the initial state value of the power system of the stateobserver AEKF_(x),

P_(θ,θ) ^(x) is the initial covariance error matrix value of the stateestimation of the state observer AEKF_(x),

Q_(θ,θ) ^(x) is the initial covariance error matrix value of the powersystem noise of the state observer AEKF_(θ),

R_(θ,θ) is the initial covariance matrix of the observation noise of thestate observer AEKF_(x);

and R_(k)=R_(k,0,L−1);

Step 3, performing time update on the parameter observer AEKF_(θ), inwhich the updated time scale is a macroscopic time scale, and gettingthe prior estimate {circumflex over (θ)}⁻ _(l) of θ at the momentt_(1,0), and

$\quad\left\{ {\begin{matrix}{{\hat{\theta}}_{1}^{-} = {\hat{\theta}}_{0}} \\{P_{1}^{0, -} = {P_{0}^{0} + Q_{0}^{0}}}\end{matrix};} \right.$

Step 4, performing time update and measurement update on the stateobserver AEKF_(x);

performing time update on the state observer AEKF_(x), in which theupdated time scale is a microscopic time scale, and obtaining the priorestimate {circumflex over (x)}⁻ _(0.3) of x at the moment t_(0.3),wherein

$\quad\left\{ {\begin{matrix}{{\hat{x}}_{0,1}^{-} = {F\left( {{\hat{x}}_{0,0}^{-},{\hat{\theta}}_{0}^{-},u_{0,1}} \right)}} \\{P_{0,1}^{x, -} = {{A_{0,1}P_{0,1}^{x}A_{0,1}^{T}} + Q_{0,1}^{x}}}\end{matrix},} \right.$

A_(0.3) is the Jacobian matrix of the state function of power system atthe moment t_(0.3) applied in electric vehicles, and

${A_{0,1} = \left. \frac{\partial{F\left( {x,{\hat{\theta}}_{0}^{-},u_{0,1}} \right)}}{\partial x} \right|_{x = {\hat{x}}_{0,1}}},$

and

T is the matrix transpose;

updating the state observer AEKF_(x) based on the measurement, andobtaining the posterior estimate {circumflex over (x)}⁻ _(0.1) of x;

updating the innovation matrix for state estimation to get:

e _(0.1) =Y _(0.1) −G({circumflex over (x)} ⁻ _(0.1), {circumflex over(θ)}⁻ _(l) ,u _(0.3)),

wherein the Kalman gain matrix is:

K _(0.1) ^(x) =P _(0.1) ^(x,−)(C _(0.3) ^(x))^(T)(C _(0.3) ^(x) P _(0.1)^(T)(C _(0.1) ^(x))^(T) =R _(θ, θ))⁻¹,

the window length function of voltage error estimation is

${H_{0,1}^{x} = {\frac{1}{M_{x}}{\sum\limits_{i = {1 - M_{x} + 1}}^{l}{e_{0,1}e_{0,1}^{T}}}}};$

updating the covariance matrix of noise:

$\left\{ {\begin{matrix}{R_{0,1} = {H_{0,1}^{x} - {C_{0,1}^{x}{P_{0,1}^{x, -}\left( C_{0,1}^{x} \right)}^{T}}}} \\{Q_{0,1}^{x} = {K_{0,1}^{x}{H_{0,1}^{x}\left( K_{0,1}^{x} \right)}^{T}}}\end{matrix};} \right.$

correcting the state estimate: {circumflex over (x)}⁻ _(0.1)={circumflexover (x)}⁻ _(0.1)=K_(0.1) ^(x)[Y_(0.1)−G({circumflex over (x)}⁻ _(0.1),{circumflex over (θ)}⁻ ₁u_(0.3))];

updating the estimate error covariance of state:

P _(0.1) ^(T)=(I−K _(0.1) ^(x) C _(0.1) ^(x))P _(0.3) ^(x,−);

where

C_(0.3) ^(x) is the Jacobian matrix of the observation function of powersystem at the moment t_(0.1) applied in electric vehicles, and

${C_{0,1}^{x} = \left. \frac{\partial{G\left( {x,{\hat{\theta}}_{1}^{-},u_{0,1}} \right)}}{\partial x} \right|_{x = {\hat{x}}_{0,1}}};$

cycling the above operations for L times until the moment of stateobserver AEKF_(x) is updated to t_(0.1), then going to the next step;

Step 5, updating the parameter observer AEKF_(θ) based on themeasurement to get the posterior estimate {circumflex over (θ)}⁻ ₁;

updating the innovation matrix for parameter estimation to get:

e ₁ ^(θ) =Y _(1.0) −G({circumflex over (x)} ⁻ _(1.0),{circumflex over(θ)}⁻ ₁ ,u _(1.0)), wherein

the Kalman gain matrix is: K₁ ^(θ)=P₁ ^(θ)−(C₁ ^(θ))^(T)(C₁ ^(θ)P₁^(θ,−)(C₁ ^(θ))^(T)+R₀)⁻¹, and

the window length function of voltage error estimation is:

${H_{1}^{\theta} = {\frac{1}{M_{\theta}}{\sum\limits_{i = {1 - M_{o} + 1}}^{l}{e_{1}^{\theta}\left( e_{1}^{\theta} \right)}^{T}}}};$

updating the covariance matrix of noise:

$\left\{ {\begin{matrix}{R_{1} = {H_{1}^{\theta} - {C_{1}^{\theta}{P_{1}^{\theta, -}\left( C_{1}^{\theta} \right)}^{T}}}} \\{Q_{1}^{\theta} = {K_{t}^{\theta}{H_{1}^{\theta}\left( K_{1}^{\theta} \right)}^{T}}}\end{matrix};} \right.$

correcting the state estimate: {circumflex over (θ)}⁻ ₁={circumflex over(θ)}⁻ _(l)+K₁ ^(θ)e₁ ^(θ);

updating the estimate error covariance of state:

P _(l) ^(θ,−)=(I−K ₁ ^(θ) C ₁ ^(θ))P ₁ ^(θ,−),

where

C₁ ^(θ) is the Jacobian matrix of the observation function of powersystem at the moment t_(1,0) applied in electric vehicles, and

${C_{1}^{0} = \left. \frac{\partial{G\left( {{\hat{x}}_{1,0},\theta,u_{1,0}} \right)}}{\partial\theta} \right|_{\theta = {\hat{x}}_{1}^{-}}};$

cycling the operations of step 3 and step 4 until the moment t_(k,l);

performing time update on the parameter observer AEKF_(θ) to get theprior estimate {circumflex over (θ)}⁻ _(k) of parameter θ at the momentt_(k,l), wherein

$\left\{ {\begin{matrix}{{\hat{\theta}}_{k}^{-} = {\hat{\theta}}_{k - 1}} \\{P_{k}^{\theta, -} = {P_{k - 1}^{\theta} + Q_{k - 1}^{\theta}}}\end{matrix};} \right.$

performing time update on the state observer AEKF_(x) to get the priorestimate {circumflex over (x)}⁻ _(k-1,l) of state {circumflex over (x)}⁻_(k-1,l) at the moment t_(k,l), wherein

$\left\{ {\begin{matrix}{{\hat{x}}_{{k - 1},l}^{-} = {F\left( {{\hat{x}}_{{k - 1},{l - 1}}^{-},{\hat{\theta}}_{k}^{-},u_{{k - 1},{l - 1}}} \right)}} \\{P_{{k - 1},l}^{x, -} = {{A_{{k - 1},{l - 1}}P_{{k - 1},{l - 1}}^{x}A_{{k - 1},{l - 1}}^{T}} + Q_{{k - 1},{l - 1}}^{x}}}\end{matrix},} \right.$

A_(0,1) is the Jacobian matrix of the state function of power system atthe moment t_(k,l) applied in electric vehicles, and

${A_{{k - 1},{l - 1}} = \left. \frac{\partial{F\left( {x,{\hat{\theta}}_{k}^{-},u_{{k - 1},l}} \right)}}{\partial x} \right|_{x = {\hat{x}}_{{k - 1},{l - 1}}}};$

updating the state observer AEKF_(x) based on the measurement to obtainthe posterior estimate {circumflex over (x)}⁻ _(k-1J) of state x at themoment t_(k,l); updating the innovation matrix for state estimation toget: e_(k-1,l)=Y_(k-1,l)G({circumflex over (x)}⁻ _(k-1,l){circumflexover (θ)}⁻ _(k)u_(k-1,l)), wherein the Kalman gain matrix is:

K _(k-1J) ^(x) =P _(k-1,l) ^(x,−)(C _(k-1,l) ^(x))^(T)(C _(k-1J) ^(x) P_(k-1,l) ^(x,−)(C _(k-1,l) ^(x))^(T)+R _(k-1/−1))⁻¹;

matching the covariance adaptively:

${H_{{k - 1},l}^{x} = {\frac{1}{M_{x}}{\sum\limits_{i = {l - M_{x} + 1}}^{l}{e_{{k - 1},l}e_{{k - 1},l}^{T}}}}};$

updating the noise covariance:

$\left\{ {\begin{matrix}{R_{{k - 1},l} = {H_{{k - 1},l}^{x} - {C_{{k - 1},l}^{x}{P_{{k - 1},l}^{x, -}\left( C_{{k - 1},l}^{x} \right)}^{T}}}} \\{Q_{{k - 1},l}^{x} = {K_{{k - 1},l}^{x}{H_{{k - 1},l}^{x}\left( K_{{k - 1},l}^{x} \right)}^{T}}}\end{matrix};} \right.$

correcting the state estimate:

{circumflex over (x)} ⁻ _(k-1,l) ={circumflex over (x)} ⁻ _(k-1,l) +K_(k-1,l) ^(x) [Y _(k-1,l) −G({circumflex over (x)} ⁻_(k-1,l),{circumflex over (θ)}⁻ _(k) ,u _(k-1,l))];

updating the error covariance of state estimate:

P _(k-1,l) ^(x,+)=(I−K _(k-1,l) ^(x) C _(k-1,l) ^(x))P _(k-1,l) ^(x,−),

where

C_(k-1,l) ^(x) is the Jacobian matrix of the observation function ofpower system at the moment t_(k,l) applied in electric vehicles, and

$C_{{k - 1},l}^{x} = \left. \frac{\partial{G\left( {x,{\hat{\theta}}_{k}^{-},u_{{k - 1},l}} \right)}}{\partial x} \right|_{x = {\hat{x}}_{k - 1}}$

updating the parameter observer AEKF_(θ) based on the measurement toobtain the posterior estimate {circumflex over (θ)}⁻ _(k) of parameter θat the moment t_(k,0:l,);

updating the innovation matrix for parameter estimation to get:

e _(k) ^(θ) =Y _(k,θ) −G({circumflex over (x)}⁻ _(k,θ),{circumflex over(θ)}⁻ _(k) ,u _(k,θ)), wherein

the Kalman gain matrix is:

K _(k-1,l) ^(x) =P _(k-1,l) ^(x,−)(C _(k-1,l) ^(x))^(T)(C _(k-1,l) ^(x)P _(k-1,l) ^(x,−)(C _(k-1,l) ^(x))^(T) +R _(k-1,l−l))⁻¹;

matching the covariance adaptively:

${H_{k}^{\theta} = {\frac{1}{M_{\theta}}{\sum\limits_{i = {1 - M_{\theta} + 1}}^{l}{e_{k}^{0}\left( e_{k}^{\theta} \right)}^{T}}}};$

updating the noise covariance:

$\left\{ {\begin{matrix}{R_{k} = {H_{k}^{\theta} - {C_{k}^{\theta}{P_{k}^{\theta, -}\left( C_{k}^{\theta} \right)}^{T}}}} \\{Q_{k}^{\theta} = {K_{k}^{\theta}{H_{k}^{\theta}\left( K_{k}^{\theta} \right)}^{T}}}\end{matrix};} \right.$

correcting the state estimate: {circumflex over (θ)}⁻ _(k)={circumflexover (θ)}⁻ _(k)+K_(k) ^(θ)e_(k) ^(θ);

updating the error covariance of state estimate:

P _(k) ^(θ,+)=(I−K _(k) ^(θ) C _(k) ^(θ))P _(k) ^(θ,−),

where

C_(k) ^(θ) is the Jacobian matrix of the observation function of powersystem at the moment t_(k,0:l,) applied in electric vehicles, and

${C_{k}^{0} = \left. \frac{\partial{G\left( {{\hat{x}}_{k,0},\theta,u_{k,0}} \right)}}{\partial\theta} \right|_{\theta = {\hat{x}}_{k}^{-}}};$

and

cycling the above operations until the estimation is completed,

the state observer AEKF_(x), in which the updated time scale is a, andobtain the prior estimate {circumflex over (x)}⁻ _(θ,l) of x at themoment t_(θ,l), and

$\left\{ {\begin{matrix}{{\hat{x}}_{0,1}^{-} = {F\left( {{\hat{x}}_{0,0}^{-},{\hat{\theta}}_{0}^{-},u_{0,1}} \right)}} \\{P_{0,1}^{x, -} = {{A_{0,1}P_{0,1}^{x}A_{0,1}^{T}} + Q_{0,1}^{x}}}\end{matrix},} \right.$

the parameter observer AEKF_(θ) to get the prior estimate {circumflexover (θ)}⁻ _(k) of parameter θ at the moment t_(k,l), and

$\left\{ {\begin{matrix}{{\hat{\theta}}_{k}^{-} = {\hat{\theta}}_{k - 1}} \\{P_{k}^{\theta, -} = {P_{k - 1}^{\theta} + Q_{k - 1}^{\theta}}}\end{matrix};} \right.$

the state observer AEKF_(x) to get the prior estimate {circumflex over(x)}⁻ _(k-1,l) of state {circumflex over (x)}⁻ _(k-1,l) at the momentt_(k,l), and

$\left\{ {\begin{matrix}{{\hat{x}}_{{k - 1},l}^{-} = {F\left( {{\hat{x}}_{{k - 1},{l - 1}}^{-},{\hat{\theta}}_{k}^{-},u_{{k - 1},{l - 1}}} \right)}} \\{P_{{k - 1},l}^{x, -} = {{A_{{k - 1},{l - 1}}P_{{k - 1},{l - 1}}^{x}A_{{k - 1},{l - 1}}^{T}} + Q_{{k - 1},{l - 1}}^{x}}}\end{matrix},} \right.$

When using this invention to estimate the power system parameter andstate of electric vehicles, in the same moment, the innovation source isthe same for the macroscopic time scale and microscopic time scale,which will be beneficial to improve the parameter and state estimatesconvergence and the estimate accuracy. The calculation time and costwill both be reduced by estimating the power system parameter and stateof electric vehicles based on the multi-scale.

Preferably, when performing time update on the state observer AEKF_(x),the cycle length of microscopic time scale is l=1:L, and when themacroscopic time scale transfers to k from k-1, the microscopic timescale will changes to 0 from L.

Preferably, the driving cycles data of the power system applied inelectric vehicles is input to the state estimation filter in real-time.In this case, the state estimation filter can estimate the parameter andstate based on the driving data closest to the real working conditionsof power system applied in electric vehicles, which can improve theestimation accuracy.

Also, this invention proposes a battery management system which can useany of the above power system state and parameter estimation methodsapplied in electric vehicles to estimate the battery parameter and stateof electric vehicles. Compared with the present mainstream batterymanagement system, the proposed battery management system has higheraccuracy, lower time-consuming and is more safe and reliable.

DESCRIPTION OF THE DRAWINGS

FIG. 1 is the schematic diagram of he proposed multi-time scale adaptiveextended Kalman filter algorithm;

FIG. 2 is the equivalent circuit diagram by equalizing the battery of anelectric vehicle to the equivalent circuit model with a first order RCnetwork;

FIG. 3 is the cycle data of a power battery applied in electricvehicles; FIG. 3(a) is the current changing curve of cell cycling; FIG.3(b) is the state of changing SoC curve of cell cycling.

FIG. 4 is the open circuit voltage curve by equalizing the battery ofelectric vehicle to the equivalent circuit model with a first order RCnetwork;

FIG. 5 is the joint estimation results of battery parameter and stateapplied in electric vehicles based on the multi-time scale, and the timescale transfer threshold is L=60 s with the battery initial SoC valuebeing 60%. FIG. 5(a) is the battery voltage estimation error curve; FIG.5(b) is the battery SoC estimation curve; FIG. 5(c) is the availablecapacity estimation curve; FIG. 5(d) is the battery available capacityestimation error curve;

FIG. 6 is the joint estimation results of battery parameter and stateapplied in electric vehicles based on the same time scale, and the timescale transfer threshold is L=1 s with the battery initial SoC valuebeing 60%. In which, FIG. 6(a) is the battery voltage estimation errorcurve; FIG. 6(b) is the battery SoC estimation curve; FIG. 6(c) is theavailable capacity estimation curve; FIG. 6(d) is the battery availablecapacity estimation error curve;

FIG. 7 is the equivalent circuit diagram by equalizing the battery ofelectric vehicle to the equivalent circuit model with second order RCnetworks;

FIG. 8 is the joint estimation results of battery parameter and stateapplied in electric vehicles based on the multi-time scale, and the timescale transfer threshold is L=60 s with the battery initial SoC valuebeing 60%. In which, FIG. 8(a) is the battery voltage estimation errorcurve; FIG. 8(b) is the battery SoC estimation curve; FIG. 8(c) is theavailable capacity estimation curve; FIG. 8(d) is the battery availablecapacity estimation error curve.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The specific operation steps of this invention to estimate the powersystem parameter and state of electric vehicles are illustrated indetails based on FIG. 1.

Step 1, build the multi-time scale power system model of electricvehicles, which is shown as (1),

$\begin{matrix}\left\{ \begin{matrix}{{x_{k,{l + 1}} = {{F\left( {x_{x,l},\theta_{k},u_{k,l}} \right)} + \omega_{k,l}}},{\theta_{k + 1} = {\theta_{k} + \rho_{k}}}} \\{Y_{k,l} = {{G\left( {x_{k,l},\theta_{k},u_{k,l}} \right)} + v_{k,l}}}\end{matrix} \right. & (1)\end{matrix}$

where,

θ indicates the power system parameter of electric vehicles, and whenthe macroscopic time scale does not change and the microscopic timescale changes to L-1 from 0, the parameter stays the same which isθ_(k)=θ_(k,0:L-1); k is the macroscopic time scale, and L is the scaletransfer threshold to transfer the macroscopic time scale to themicroscopic time scale, which is t_(k,0)=t_(k-l,0)+L×Δt where Δt is amicroscopic time scale;

x is a hidden state of the power system of electric vehicles;

F(x_(k,l),θ_(k),u_(k,l)) is the power system state function of electricvehicles at the moment t_(k,l);

G(x_(k,l),θ_(k),u_(k,l)) is the power system observation function ofelectric vehicles at the moment t_(k,l);

x_(k,l) is the power system state of electric vehicles at the momentt_(k,l), where l is the microscopic time scale and 1≦l≦L,

t _(k,l) =t _(k,0) +l×Δt(1≦l≦L);

u_(k,l) is the input information (control matrix) to the state estimatefilter by the power system of electric vehicles, where the inputinformation includes power system current, battery voltage and SoC:

Y_(k,l) is the observation matrix (measurement matrix) of the powersystem of electric vehicles, where the observation matrix includes thebattery voltage, SoC and available capacity of the power system appliedin electric vehicles;

ω_(k,l) is the state white noise of the power system of electricvehicles at the moment t_(k,l), and its covariance matrix is Q_(k,l)^(x),

ρ_(k) is the parameter white noise of the power system of electricvehicles at the moment t_(k,l), and its covariance matrix is Q_(k) ^(θ),

ν_(k,l) is the measurement white noise of the power system of electricvehicles at the moment t_(k,l), and its covariance is R_(k,l).

Step 2, initialize the parameter observer AEKF_(θ) based on themacroscopic time scale and the state observer AEKF_(x) based on themicroscopic time scale of the power system applied in electric vehicles.

Specifically, initialize the parameter θ_(k), P_(k) ^(θ), Q_(k) ^(θ) andR_(k) of the parameter observer AEKF_(θ) to obtain θ₀, P_(θ) ^(θ), Q_(θ)^(θ) and R_(θ), where,

θ₀ is the initial parameter value of the power system of electricvehicles,

P₀ ^(θ)is the initial value of error covariance matrix P_(k) ^(θ) of thepower system parameter estimate applied in electric vehicles,

Q₀ ^(θ) is the initial value of error covariance matrix Q_(k) ^(θ) ofthe power system noise applied in electric vehicles,

R₀ is the initial value of observation noise covariance R_(k) of theparameter observer AEKF₀.

Initialize the parameter x_(k,l), P_(k,l) ^(x), Q_(k,l) ^(x) and R_(k,l)of the state observer AEKF_(x) to obtain x_(θ,θ), P_(θ,θ) ^(x), Q_(θ,θ)^(x) and R_(θ,θ), where,

x_(θ,θ) is the initial value of power system state x_(k,l) of electricvehicles,

P_(θ,θ) ^(x) is the initial value of state estimation error covarianceP_(k,l) ^(x) of the power system applied in electric vehicles,

Q_(θ,θ) ^(x) is the initial value of system noise covariance Q_(k,l)^(x) the power system of electric vehicles,

R_(θ,θ) is the initial value of system noise covariance R_(k,l) thestate observer AEKF_(x),

As the parameter observer AEKF_(θ) and state observer AEKF_(x) has therelationship as R_(k)=R_(k,0.L−1), herein R_(θ)=R_(θ,θ).

Step 3, perform time update on the parameter observer AEKF_(θ) based onthe macroscopic time scale which is prior parameter estimation with amacroscopic time scale to obtain the prior estimate {circumflex over(θ)}⁻ _(l) of θ at the moment t_(1,θ), wherein

$\begin{matrix}\left\{ {\begin{matrix}{{\hat{\theta}}_{1}^{-} = {\hat{\theta}}_{0}} \\{P_{1}^{\theta, -} = {P_{0}^{\theta} + Q_{0}^{\theta}}}\end{matrix}.} \right. & (2)\end{matrix}$

Step 4, perform time update and measurement update of the state observerAEKF_(x).

Firstly, perform time update on the state observer AEKF_(θ) based on themicroscopic time scale which is prior parameter estimation with amicroscopic time scale Δt to obtain the prior estimate {circumflex over(x)}⁻ _(θ,l) of x at the moment t_(θ,1), wherein

$\begin{matrix}\left\{ {\begin{matrix}{{\hat{x}}_{0,1}^{-} = {F\left( {{\hat{x}}_{0,0}^{-},{\hat{\theta}}_{0}^{-},u_{0,1}} \right)}} \\{P_{0,1}^{x, -} = {{A_{0,1}P_{0,1}^{x}A_{0,1}^{T}} + Q_{0,1}^{x}}}\end{matrix},} \right. & (3)\end{matrix}$

A_(θ,1) is the Jacobian matrix of state function of the power systemapplied in electric vehicles in the estimation process,

$\begin{matrix}{{A_{0,1} = \left. \frac{\partial{F\left( {x,{\hat{\theta}}_{0}^{-},u_{0,1}} \right)}}{\partial x} \right|_{x = {\hat{x}}_{0,1}}},} & (4)\end{matrix}$

and

T represents the matrix transpose.

Then, update the state observer AEKF_(x) based on the microscopic timescale to obtain the posterior estimate {circumflex over (x)}⁻ _(θ,l).

Update the innovation matrix of state estimation to get:

e _(θ,l[=Y) _(θ,1) −G({circumflex over (x)} ⁻ _(θ,1),{circumflex over(θ)}⁻ _(l) ,u _(θ,1))   (5),

wherein

the Kalman gain matrix is:

K _(θ,l) ^(x) =P _(θ,l) ^(x,−)(C _(θ,3) ^(x))^(x)(C _(θ,3) ^(x) P ^(x,−)_(θ,l)(C _(θ,l) ^(x))^(x) +R _(θ,θ))⁻¹   (6) and

the window length function of voltage estimation error (which is alsocalled adaptive covariance matching) is:

$\begin{matrix}{H_{0,1}^{x} = {\frac{1}{M_{x}}{\sum\limits_{i = {1 - M_{x} + 1}}^{l}{e_{0,1}{e_{0,1}^{T}.}}}}} & (7)\end{matrix}$

Update the noise covariance to get:

$\begin{matrix}\left\{ {\begin{matrix}{R_{0,1} = {H_{0,1}^{x} - {C_{0,1}^{x}{P_{0,1}^{x, -}\left( C_{0,1}^{x} \right)}^{T}}}} \\{Q_{0,1}^{x} = {K_{0,1}^{x}{H_{0,1}^{x}\left( K_{0,1}^{x} \right)}^{T}}}\end{matrix}.} \right. & (8)\end{matrix}$

Correct the state estimate to get:

{circumflex over (x)} ⁻ _(θ,l) ={circumflex over (x)} ⁻ _(θ,1) +K ^(x)_(θ,l) [Y _(θ,l) −G({circumflex over (x)} ⁻ _(θ,l), {circumflex over(θ)}⁻ _(l) ,u _(θ,l))]  (9)

Update the error covariance of state estimation:

P ^(x,−) _(θ,l)=(I−K ^(x) _(θ,l) C ^(x) _(θ,l))P ^(x,−) _(θ,l)   (10),

where

C^(x) _(θ,l) is the Jacobian matrix of the observation function at themoment t_(θ,l) of the power system applied in the electric vehicles inthe state estimation process, and

$\begin{matrix}{C_{0,1}^{x} = \left. \frac{\partial{G\left( {x,{\hat{\theta}}_{1}^{-},u_{0,1}} \right)}}{\partial x} \middle| {}_{x = {\hat{x}}_{0,1}}. \right.} & (11)\end{matrix}$

Cycle the above operation for L times to update the state observerAEKF_(x) based on the microscopic time scale to moment t_(θ,l) which ist_(1,θ), then turn to the next step.

Step 5, update the state observer AEKF_(θ) based on the macroscopic timescale to obtain the posterior estimate {circumflex over (θ)}⁻ _(l) ofparameter θ at the moment t_(1,0).

Update the innovation matrix of parameter estimation to get:

e ^(θ) _(l) =Y _(1,0) −G({circumflex over (x)} ⁻ _(1,0),{circumflex over(θ)}⁻ _(l) ,u _(1,0))   (12).

The Kalman gain matrix is:

K ^(θ) _(l) =P ^(θ,−) _(l)(C ^(θ) _(l))^(x)(C ^(θ) _(l) P ^(θ,−) _(l)(C^(θ) _(l))^(x) +R _(θ))⁻¹   (13)

The window length function of voltage estimation error which is adaptivecovariance matching is:

$\begin{matrix}{H_{1}^{\theta} = {\frac{1}{M_{0}}{\sum\limits_{i = {1 - M_{o} + 1}}^{l}{{e_{1}^{\theta}\left( e_{1}^{\theta} \right)}^{T}.}}}} & (14)\end{matrix}$

Update the noise covariance to get:

$\begin{matrix}\left\{ {\begin{matrix}{R_{1} = {H_{1}^{\theta} - {C_{1}^{\theta}{P_{1}^{\theta, -}\left( C_{1}^{\theta} \right)}^{T}}}} \\{Q_{1}^{\theta} = {K_{1}^{\theta}{H_{1}^{\theta}\left( K_{1}^{\theta} \right)}^{T}}}\end{matrix}.} \right. & (15)\end{matrix}$

Correct the state estimate to get:

{circumflex over (θ)}⁻ _(l)=θ₁ +K ^(θ) _(l) e ^(θ) _(l)   (16).

Update the error covariance of state estimation:

P ^(θ,−) _(l)=(I−K ^(θ) _(l) C ^(θ) _(l))P ^(θ,−) _(l)   (17)

where,

C^(θ) _(l) is the Jacobian matrix of the observation function at themoment t_(1,0) of the power system applied in the electric vehicles inthe state estimation process, in which C^(θ) _(l) is the partialdifferential equation about state of the observation function of thepower system applied in electric vehicles, so

$\begin{matrix}{C_{1}^{\theta} = \left. \frac{\partial{G\left( {{\hat{x}}_{1,0},\theta,u_{1,0}} \right)}}{\partial\theta} \middle| {}_{\theta = {\hat{x}}_{1}^{-}}. \right.} & (18)\end{matrix}$

Cycle the operation of step 3 and step 4 until the moment t_(k,l).

Perform time update on the parameter observer AEKF_(θ) based on themacroscopic time scale to get the prior estimate {circumflex over (θ)}⁻_(k) of parameter θ at the moment t_(k,l), wherein

$\begin{matrix}\left\{ {\begin{matrix}{{\hat{\theta}}_{k}^{-} = {\hat{\theta}}_{k - 1}} \\{P_{k}^{\theta, -} = {P_{k - 1}^{\theta} + Q_{k - 1}^{\theta}}}\end{matrix}.} \right. & (19)\end{matrix}$

Perform time update on the state observer AEKF_(θ) based on themicroscopic time scale to get the prior estimate {circumflex over (x)}⁻_(k-1,l) of state x at the moment t_(k,l), wherein

$\begin{matrix}\left\{ {\begin{matrix}{{\hat{x}}_{{k - 1},l}^{-} = {F\left( {{\hat{x}}_{{k - 1},{l - 1}}^{-},{\hat{\theta}}_{k}^{-},u_{{k - 1},{l - 1}}} \right)}} \\{P_{{k - 1},l}^{x, -} = {{A_{{k - 1},{l - 1}}P_{{k - 1},{l - 1}}^{x}A_{{k - 1},{l - 1}}^{T}} + Q_{{k - 1},{l - 1}}^{x}}}\end{matrix},} \right. & (20)\end{matrix}$

A_(k-1,l-1) the Jacobian matrix of the state function at the momentt_(k,l) of the power system applied in the electric vehicles in thestate estimation process, and

$\begin{matrix}{A_{{k - 1},{l - 1}} = {\left. \frac{\partial{F\left( {x,{\hat{\theta}}_{k}^{, -},u_{{k - 1},l}} \right)}}{\partial x} \middle| x \right. = {{\hat{x}}_{{k - 1},{l - 1}}.}}} & (21)\end{matrix}$

Update the state observer AEKF_(x) according to the measurement based onthe microscopic time scare to get the posterior estimate {circumflexover (x)}⁻ _(k-1,l) of state x at the moment t_(k,l).

Update the innovation matrix of state estimation to get:

e _(k-1,l) =Y _(k−1,l−) G({circumflex over (x)} ⁻ _(k-1,l),{circumflexover (θ)}⁻ _(k) ,u _(k-1,l))   (22).

The Kalman gain matrix is:

K ^(x) _(k-1,l) =P ^(x,−) _(k-1,l)(C ^(x) _(k-1,l))^(T)(C ^(x,−)_(k-1,l) P ^(x,−) _(k-1,l)(C ^(x) _(k-1,l))^(T) +R _(k-1,l-1))⁻¹   (23).

Match the covariance adaptively to get:

$\begin{matrix}{H_{{k - 1},l}^{x} = {\frac{1}{M_{x}}{\sum\limits_{i = {l - M_{x} + 1}}^{l}\; {e_{{k - 1},l}{e_{{k - 1},l}^{T}.}}}}} & (24)\end{matrix}$

Update the noise covariance to get:

$\begin{matrix}\left\{ {\begin{matrix}{R_{{k - 1},l} = {H_{{k - 1},l}^{x} - {C_{{k - 1},l}^{x}{P_{{k - 1},l}^{x, -}\left( C_{{k - 1},l}^{x} \right)}^{T}}}} \\{Q_{{k - 1},l}^{x} = {K_{{k - 1},l}^{x}{H_{{k - 1},l}^{x}\left( K_{{k - 1},l}^{x} \right)}^{T}}}\end{matrix}.} \right. & (25)\end{matrix}$

Correct the state estimate to get:

{circumflex over (x)} ⁻ _(k-1,l) ={circumflex over (x)} ⁻ _(k-1,l) +K^(x) _(k-1,l) [Y _(k-1,l) −G({circumflex over (x)} ⁻ _(k-1,l),{circumflex over (θ)}⁻ _(k) ,u _(k-1,l))]  (26).

Because {circumflex over (x)}_(k,0)={circumflex over (x)}_(k-1,L), so

$\begin{matrix}{\frac{{\hat{x}}_{k,0}}{{\hat{\theta}}_{k}^{-}} = {\frac{{\hat{x}}_{{k - 1},L}^{+}}{{\hat{\theta}}_{k}^{-}} = {{\quad\quad}{\quad{{\frac{}{{\hat{\theta}}_{k}^{-}}\left( {{\hat{x}}_{{k - 1},L}^{-} + {K_{{k - 1},{L - 1}}^{x}\left( {Y_{{k - 1},{L - 1}} - {G\left( {{\hat{x}}_{{k - 1},L}^{-},{{\hat{\theta}}_{k,}^{-}u_{{k -},{L - 1}}}} \right)}} \right)}} \right)},}}}}} & (27) \\{\mspace{79mu} {{{\frac{}{{\hat{\theta}}_{k}^{-}}\left( {K_{{k - 1},{L - 1}}^{x}Y_{{k - 1},{L - 1}}} \right)} = {Y_{{k - 1},{L - 1}}\frac{\partial K_{{k - 1},{L - 1}}^{x}}{\partial{\hat{\theta}}_{k}^{-}}}},\mspace{20mu} {and}}} & (28) \\{{\frac{}{{\hat{\theta}}_{k}^{-}}\left( {K_{{k - 1},{L - 1}}^{x}{G\left( {{\hat{x}}_{{k - 1},{L - 1}}^{-},{\hat{\theta}}_{k}^{-},u_{{k - 1},{L - 1}}} \right)}} \right)} = {{K_{{k - 1},{L - 1}}^{x}\frac{{G\left( {{\hat{x}}_{{k - 1},{L - 1}}^{-},{\hat{\theta}}_{k}^{-},u_{{k - 1},{L - 1}}} \right)}}{{\hat{\theta}}_{k}^{-}}} + {\frac{\partial K_{{k - 1},{L - 1}}^{x}}{\partial{\hat{\theta}}_{k}^{-}}{{G\left( {{\hat{x}}_{{k - 1},{L - 1}}^{-},{\hat{\theta}}_{k}^{-},u_{{k - 1},{L - 1}}} \right)}.}}}} & (29)\end{matrix}$

Update the error covariance of state estimation to get:

P ^(x,−) _(k-1,l)=(I−K ^(x) _(k-1,l) C ^(x) _(k-1,l))P ^(x,−) _(k-1,l)  (30),

where,

C^(x) _(k-1,l) is the Jacobian matrix of the observation function at themoment t_(k,l) of the power system applied in the electric vehicles inthe state estimation process, and

$\begin{matrix}{C_{{k - 1},l}^{x} = {\left. \frac{\partial{G\left( {x,{\hat{\theta}}_{k}^{-},u_{{k - 1},l}} \right)}}{\partial x} \middle| x \right. = {\hat{x}}_{{k - 1},l}}} & (31)\end{matrix}$

Update the parameter observer AEKF_(θ) according to the measurementbased on the macroscopic time scale to get the posterior estimate{circumflex over (θ)}⁻ _(k) of parameter θ at the moment t_(k,θ1).

Update the innovation matrix of parameter estimation to get:

e ^(θ) _(k) =Y _(k,θ) −G({circumflex over (x)} ⁻ _(k,θ),{circumflex over(θ)}⁻ _(k) ,u _(k,θ))   (32).

The Kalman gain matrix is

K ^(θ) _(k) =P ^(θ,−) _(k)(C ^(θ) _(k))^(T)(C ^(θ) _(k) P ^(θ,−) _(k)(C^(θ) _(k))^(x) +R _(k-1))⁻¹   (33).

Match the covariance adaptively to get:

$\begin{matrix}{H_{k}^{\theta} = {\frac{1}{M_{\theta}}{\sum\limits_{i = {1 - M_{\theta} + 1}}^{l}\; {{e_{k}^{\theta}\left( e_{k}^{\theta} \right)}^{T}.}}}} & (34)\end{matrix}$

Update the noise covariance to get:

$\begin{matrix}\left\{ {\begin{matrix}{R_{k} = {H_{k}^{\theta} - {C_{k}^{\theta}{P_{k}^{\theta, -}\left( C_{k}^{\theta} \right)}^{T}}}} \\{Q_{k}^{\theta} = {K_{k}^{\theta}\left( K_{k}^{\theta} \right)}^{T}}\end{matrix}.} \right. & (35)\end{matrix}$

Correct the state estimate to get:

{circumflex over (θ)}⁻ _(k)={circumflex over (θ)}⁻ _(k) +K ^(θ) _(k) e^(θ) _(k)   (36).

Update the error covariance of state estimation to get:

P ^(θ,−) _(k)=(I−K ⁻ _(k) C ^(θ) _(k))P ^(θ,−) _(k)   (37),

where,

C^(θ) _(k) is the Jacobian matrix of the observation function at themoment t_(k,θ,l) of the power system applied in the electric vehicles inthe state estimation process, and

$\begin{matrix}{C_{k}^{\theta} = \left. \frac{\partial{G\left( {{{\hat{x}}_{k,0,}\theta},u_{k,0}} \right)}}{\partial\theta} \middle| {}_{\theta = {\hat{x}}_{k}^{-}}. \right.} & (38)\end{matrix}$

Cycle the above operation until the estimation is completed.

In the calculation process, after the parameter and state estimate atthe moment k is finished, the time of the state estimation filter willincrease to (k)=(k+1)⁻ from (k)⁺, and get ready for the state estimationat moment (k+1), when x_(k,θ)=x⁻ _(k,θ), {circumflex over(θ)}_(k)={circumflex over (θ)}⁻ _(k).

When applying the described estimation method to estimate the parameterand state of the power system applied in electric vehicles, the drivingcycles data of the power system applied in electric vehicles is input tothe state estimation filter in real-time to make the state estimationfilter estimate the parameter and state based on the driving dataclosest to the real working conditions of power system applied inelectric vehicles to improve the estimation accuracy. Obviously, thereal-time performance of battery parameter is very meaningful to ensurethe reliability and accuracy of he battery state estimate.

Besides, in the estimation process, at the same moment, the innovationbased on the macroscopic time scale and microscopic time scale comesfrom the same voltage observation error of the power system applied inelectric vehicles. In this case, the convergence of parameter estimateand state estimate, as well as the estimation accuracy, can be improved.

Embodiment 1

In the following, an example of estimating the battery parameter andstate applied in electric vehicles will be provided to illustrate theadvantage of applying this invention to obtain the parameters and stateof the power system of the electric vehicle.

The battery applied in electric vehicles is equalized to the equivalentcircuit model with a first order RC network, which is shown as FIG. 2,and the state function and observation function are built as (39),

$\begin{matrix}\left\{ {\begin{matrix}{x_{k,{l + 1}} = {{F\left( {x_{k,l},\theta_{k},u_{k,l}} \right)} + \omega_{k,l}}} \\{Y_{k,l} = {{G\left( {x_{k,l},\theta_{k},u_{k,l}} \right)} + v_{k,l}}}\end{matrix},} \right. & (39)\end{matrix}$

So,

$\begin{matrix}\left\{ {\begin{matrix}\begin{matrix}{x_{k,{l + 1}} = {{\begin{bmatrix}{\exp \left( {- \frac{T_{t}}{R_{D}C_{D}}} \right)} & 0 \\0 & 1\end{bmatrix}x_{k,l}} +}} \\{{\begin{bmatrix}{\left( {1 - {\exp \left( {- \frac{1}{R_{D}C_{D}}} \right)}} \right)R_{D}} \\{- \frac{T_{t}}{C_{a}}}\end{bmatrix}u_{k,{l + 1}}} + \omega_{k,{l + 1}}}\end{matrix} \\{Y_{k,l} = {{g\left( {{x(2)},C_{a}} \right)} - {x(1)} - {R_{l}u_{k,l}} + v_{k,l}}}\end{matrix},} \right. & (40)\end{matrix}$

where,

T_(t) is the sampling time,

R_(p) is the battery polarization resistance,

C_(D) is the battery polarization capacitance,

R_(i) is the battery ohmic resistance,

C_(a) is the battery available capacity,

g(x(2),C_(a)) is the battery open circuit model:

The battery parameter to estimate is θ=[R_(D)C_(D)R_(i)C_(a)], where

x is the battery state to estimate, and the state x includes x(1)−U_(D)and x(2)−SoC. U_(D) the battery polarization voltage.

The sampling time T_(l) is set as 1 s (second). The battery current dataof driving cycles by the battery experiment is shown in FIG. 3(a). Itcan be seen that the battery current fluctuates strongly in the drivingcycles and the maximum value is up to 70 A (Ampere). FIG. 3(b) shows thebattery cell SoC curve in cycles. In which, the battery SoC decreasescontinually in the driving cycles and the slight fluctuation has beenobserved with the falling process. The battery open circuit voltagecurve is shown in FIG. 4. It can be seen that the battery SoC decreasesas the open circuit voltage falls, and the available capacity is 31.8 Ah(Ampere hour).

The estimation results are shown in FIG. 5 by applying the invention toestimate the battery parameter and state jointly, in which the timescale L is set to 60 s, and the sampling points is 2000. Based on theabove, the following conclusions can be made.

Firstly, the convergent battery voltage estimation error, SoC estimationerror and available capacity estimation error are respectivelyeffectively limited within 25 mV, 0.5% and 0.5 Ah with the inaccuratebattery available capacity and initial SoC value applied in electricvehicles. It shows that the available capacity estimate is tendingtowards stability gradually by using the same innovation source at thesame moment to estimate the battery parameter change based on themacroscopic time scale and battery state change based on the microscopictime scale. After convergence, the available capacity estimation erroris within 0.5 Ah, whose accuracy is much higher than the designrequirement of the present mainstream battery management system appliedin electric vehicles. This invention related to the parameter and stateestimation method of a power system of an electric vehicle can be usedto estimate the battery parameters and state of the battery managementsystem applied in electric vehicles.

Secondly, the change of battery available capacity estimation result isstable, which will not shake in spite of the uncertain current or powerexcitation, and will converge to the test-obtained reference veryquickly.

Thirdly,the calculation time cost is 2.512 s.

In conclusion, the invented estimation method possesses good correctioncapability against inaccurate battery available capacity and initial SoCvalues, and the calculation time for estimation is 2.512 s, indicatingthe high-speed calculation ability.

Embodiment for Comparison

The invented estimation method is applied to estimate the batteryparameter and state jointly of electric vehicles with the time scalebeing 1 s, and the sampling points being 21,000. During the estimationprocess, as the time scale L is set to 1 s, the method which bases themulti-time scale to realize the joint estimation of battery parameterand state will degrade to the single time scale joint estimation ofbattery parameter and state, and the estimation results are shown inFIG. 6. The following conclusions can be made.

Firstly, the battery voltage estimation error, SoC estimation error andthe available capacity error are respectively less than 40 mV(millivolt), 1% and 1 Ah. That is the available capacity estimationerror is less than 1Ah/31.8 Ah=3.1%. It shows that the availablecapacity estimate is tending towards stability gradually by using thesame innovation source at the same moment to estimate the batteryparameter change based on the macroscopic time scale and battery statechange based on the microscopic time scale. After convergence, theavailable capacity estimation error is within 1 Ah, whose accuracy ishigher than the design requirement of the present mainstream batterymanagement system applied in electric vehicles.

Secondly, the maximum convergent estimation errors of battery voltage,SOC and available capacity are respectively less than 35 mV, 1% and 1Ah. It can be observed that the high estimation accuracy is obtainedwhen using this invention to estimate battery SoC and availablecapacity, which indicates that the battery parameter and stateestimation accuracy can still be guaranteed even based on the initialSoC and available capacity with large error.

Thirdly, the voltage and available capacity estimation results fluctuategreatly with large battery working current. From FIG. 6(a) and FIG.6(c), it can be seen that the obvious spike indicates the moment whenthe battery transfers to rest state from with big current excitation.Because the same innovation source is applied to estimate the batteryparameter and state, the available capacity estimation is tendingtowards stability, and the available capacity error is within 1 Ah afterfull convergence.

Fourthly, the calculation time cost is 4.709 s.

In conclusion, the invented estimation method possesses good correctioncapability against inaccurate battery available capacity and initial SoCvalues, and the calculation time for estimation is 4.709 s, indicatingthe high-speed calculation ability.

By comparing FIG. 5 and FIG. 6, it can be seen that the joint estimationresults of battery parameter and state based on the multi-time scalepossesses higher accuracy than the joint estimation results of batteryparameter and state based on the single time scale, which will result insafe, reliable, and efficient work of the battery management system.Besides, the available capacity and SoC will converge to thetest-obtained reference more quickly and reliably with erroneousavailable capacity and initial SoC value, indicating its effectivecapability to solve the non-convergence problem. Also, the convergentestimation errors of battery voltage, SoC and available capacity are allwithin 1%, whose estimation accuracy is much higher than that of thebattery SoC and available capacity estimation of the present mainstreambattery management system applied in electric vehicles. Furthermore, thecalculation time decreased to 2.512 s from 4.709 s, which has reducedthe calculation cost of the battery management system by saving 47%calculation time.

Embodiment 2

The electric battery is equalized to the equivalent circuit model withsecond order RC networks, which is illustrated in FIG. 7. The statefunction and observation function of the equivalent circuit model areshown as (41),

$\begin{matrix}\left\{ \begin{matrix}{\begin{matrix}{x_{k,{l + 1}} = {{\begin{bmatrix}{\exp \left( {- \frac{T_{t}}{R_{D\; 1}C_{D\; 1}}} \right)} & 0 & 0 \\0 & {\exp \left( {- \frac{T_{t}}{R_{D\; 2}C_{D\; 2}}} \right)} & 0 \\0 & 0 & 1\end{bmatrix}x_{k,l}} +}} \\{\quad{{\begin{bmatrix}{\left( {1 - {\exp \left( {- \frac{1}{R_{D\; 1}C_{D\; 1}}} \right)}} \right)R_{D\; 1}} \\{\left( {1 - {\exp \left( {- \frac{T_{t}}{{R_{D\; 2}C_{D\; 2}}\;}} \right)}} \right)R_{D\; 2}} \\{- \frac{T_{t}}{C_{a}}}\end{bmatrix}u_{k,{l + 1}}} + \omega_{k,{l + 1}}}}\end{matrix},} \\{Y_{k,l} = {{g\left( {{x(3)},C_{a}} \right)} - {x(1)} - {x(2)} - {R_{l}u_{k,l}} + v_{k,l}}}\end{matrix} \right. & (41)\end{matrix}$

where,

R_(D1) and R_(D2) are the polarization resistances,

C_(D1) and C_(D2) are the polarization capacitances,

R_(i) is the battery ohmic resistance,

C_(a) is the battery available capacity,

g (x(3),C_(a)) is the battery open circuit model;

the battery parameter to estimate is θ=[R_(D)C_(D)R_(i)C_(a)],

x is the battery state to estimate, and the state x includesx(1)−U_(D1), x(2)−U_(D2) and x(3)−SoC, U_(D1) and U_(D2) are the batterypolarization voltages.

The invention is applied to estimate the battery parameter and statejointly with the time scale being 6 s, and the sampling points being21,000. The estimation results are plotted in FIG. 8. From FIG. 8, thefollowings can be concluded.

Firstly, the convergent estimation errors of battery voltage, SoC andavailable capacity have been respectively effectively limited within 30mV, 1% and 0.5 Ah, even with inaccurate battery available capacity andinitial SoC value applied in electric vehicles. It shows that theavailable capacity estimate is tending towards stability gradually byusing the same innovation source at the same moment to estimate thebattery parameter change based on the macroscopic time scale and batterystate change based on the microscopic time scale. After convergence, theavailable capacity estimation error is within 0.5 Ah, whose accuracy ismuch higher than the design requirement of the present mainstreambattery management system applied in electric vehicles. Herein, thisinvention related to the power system parameter and state estimationmethod of electric vehicles can be used to estimate the batteryparameter and state of the battery management system applied in electricvehicles,

Secondly, the change of battery available capacity estimation result isstable, which will not shake in spite of the uncertain current or powerexcitation, and will converge to the test-obtained reference veryquickly.

Thirdly, the calculation time cost is 4.084 s

By comparing the estimation results of Embodiment 1 and Embodiment 2, itcan be known that the two estimation accuracies are close to each other.However, adding more RC networks to the equivalent circuit model willincrease the calculation time, which will then increase the calculationcost.

We claim:
 1. A method for estimating the parameters and the state of apower system of an electric vehicle, comprising the following steps of:Step 1, constructing a multi-time scale model of the power system$\left\{ {\begin{matrix}{{x_{k,{l + 1}} = {{F\left( {x_{k,l},\theta_{k},u_{k,l}} \right)} + \omega_{k,l}}},{\theta_{k + 1} = {\theta_{k} + \rho_{k}}}} \\{Y_{k,l} = {{G\left( {x_{k,l},\theta_{k},u_{k,l}} \right)} + v_{k,l}}}\end{matrix},} \right.$ in which θ indicates the parameters of the powersystem, x indicates a hidden state of the power system,F(x_(k,l),θ_(k),u_(k,l)) indicates a state function of the multi-timescale model, G(x_(k,l),θ_(k),u_(k,l)) indicates an observation functionof the multi-time scale model, x_(k,l) is the power system state atmoment t_(k,l)=t_(k,θ)+l×Δt(1≦l≦L), and k is the macroscopic time scale,l is the microscopic time scale, L is the transfer threshold between themicroscopic and macroscopic time scale. u_(k,l) is the input informationof the power system at a moment t_(k,l), Y_(k,l) is the measurementmatrix of the power system at a moment t_(k,l), ω_(k,l) is the whitenoise of the power system state, its mean is zero and its covariance isQ^(θ) _(k), ρ_(k,l) is the white noise of the power system parameter,its mean is zero and its covariance is Q^(θ) _(k), ν_(k,l) is themeasurement white noise of the power system, its mean is zero and itscovariance is R_(k,l), and θ_(k)=θ_(k,θ,l-1); Step 2, initialing θ_(u),P^(θ) ₀, Q^(θ) ₀ and R₀ of the parameter observer AEKF_(θ) based on themacroscopic time scale, in which θ₀ is the parameter initial value ofthe parameter observer AEKF_(θ), P^(θ) ₀ is the initial covariance errormatrix value of the parameter estimation of the parameter observerAEKF_(θ), Q^(θ) ₀ is the initial covariance error matrix value of thepower system noise of the parameter observer AEKF_(θ), R_(D) is theobservation noise of the parameter observer AEKF_(θ); initializingx_(θ,θ), P^(x) _(θ,θ), and R_(θ,θ) of the state observer AEKF_(x) basedon the microscopic time scale, in which, x_(θ,θ) is the initial statevalue of the power system of the state observer AEKF_(x), P^(x) _(θ,θ)is the initial covariance error matrix value of the state estimation ofthe state observer AEKF_(x), Q^(x) _(θ,θ) is the initial covarianceerror matrix value of the power system noise of the state observerAEKF_(θ), R_(θ,θ) the initial covariance matrix of the observation noiseof the state observer AEKF_(x); and R_(k)=R_(k,θ,l−1); Step 3,performing time update on the parameter observer AEKF_(θ), in which theupdated time scale is a macroscopic time scale, and getting the priorestimate {circumflex over (θ)}⁻ _(l) of θ at the moment t_(l,θ), and$\left\{ {\begin{matrix}{{\hat{\theta}}_{1}^{-} = {\hat{\theta}}_{0}} \\{P_{1}^{\theta, -} = {P_{0}^{\theta} + Q_{0}^{\theta}}}\end{matrix};} \right.$ Step 4, performing time update and measurementupdate on the state observer AEKF_(x): performing time update on thestate observer AEKF_(x), in which the updated time scale is amicroscopic time scale, and obtaining the prior estimate {circumflexover (x)}_(θ,l) of x at the moment t_(θ,l), wherein$\left\{ {\begin{matrix}{{\hat{x}}_{0,1}^{-} = {F\left( {{\hat{x}}_{0,0}^{-},{\hat{\theta}}_{0}^{-},u_{0,1}} \right)}} \\{P_{0,1}^{x, -} = {{A_{0,1}P_{0,1}^{x}A_{0,1}^{T}} + Q_{0,1}^{x}}}\end{matrix},} \right.$ A_(θ,l) is the Jacobian matrix of the statefunction of power system at the moment t_(θ,l) applied in electricvehicles, and${A_{0,1} = \left. \frac{\partial{F\left( {x,{\hat{\theta}}_{0}^{-},u_{0,1}} \right)}}{\partial x} \right|^{x = {\hat{x}}_{0,1}}},$and T is the matrix transpose; updating the state observer AEKF_(x)based on the measurement, and obtaining the posterior estimate{circumflex over (x)}⁻ _(θ,l) of x, updating the innovation matrix forstate estimation to get:e _(θ,1) =Y _(θ,1) −G({circumflex over (x)} ⁻ _(θ,1), {circumflex over(θ)}⁻ _(l) ,u _(θ,l)), wherein the Kalman gain matrix is:K ^(x) _(θ,l) =P ^(x,−) _(θ,l)(C ^(x) _(θ,l))^(T)(C ^(x) _(θ,l) P ^(x,−)_(θ,l)(C ^(x) _(θ,l))^(T) +R _(θ,θ))⁻¹, and the window length functionof voltage error estimation${H_{0,1}^{x} = {\frac{1}{M_{x}}{\sum\limits_{{i = {1 - M}},{+ 1}}^{l}\; {e_{0,1}e_{0,1}^{T}}}}};$updating the covariance matrix of noise: $\left\{ {\begin{matrix}{R_{0,1} = {H_{0,1}^{x} - C_{0,1}^{x} - {P_{0,1}^{x, -}\left( C_{0,1}^{x} \right)}^{T}}} \\{Q_{0,1}^{x} = {K_{0,1}^{x}{H_{0,1}^{x}\left( K_{0,1}^{x} \right)}^{T}}}\end{matrix};} \right.$ correcting the state estimate: {circumflex over(x)}⁻ _(θ,l)={circumflex over (x)}_(θ,l)+K^(x)_(θ,l)[Y_(θ,l)−G({circumflex over (x)}⁻ _(θ,l),{circumflex over(θ)}₁,u_(θ,1))]: updating the estimate error covariance of state:P ^(x,−) _(θ,1)=(I−K ^(x) _(θ,1) C ^(x) _(θ,1))P ^(x,−) _(θ,l), whereC^(x) _(θ,l) is the Jacobian matrix of the observation function of powersystem at the moment t_(θ,l) applied in electric vehicles, and${C_{0,1}^{x} = {\frac{\partial{G\left( {x,{\hat{\theta}}_{1}^{-},u_{0,1}} \right)}}{\partial x}_{x = {\hat{x}}_{0,1}}}};$cycling the above operations for L times until the moment of stateobserver AEKF_(x) is updated to t_(θ,l), then going to the next step;Step 5, updating the parameter observer AEKF_(θ) based on themeasurement to get the posterior estimate {circumflex over (θ)}⁻ _(l);updating the innovation matrix for parameter estimation to get:e ^(θ) _(l) =Y _(1,0) −G({circumflex over (x)} ⁻ _(1,θ),{circumflex over(θ)}⁻ _(l) ,u _(1,θ)), wherein the Kalman gain matrix is: K^(θ)₁=P^(θ,−) _(l)(C^(θ) _(l))^(T)(C^(θ) _(l)P^(θ−) _(l)(C^(θ)_(l))^(T)+R_(u))⁻¹, and the window length function of voltage errorestimation is:${H_{1}^{\theta} = {\frac{1}{M_{\theta}}{\sum\limits_{i = {1 - M_{\theta} + 1}}^{l}\; {e_{1}^{\theta}\left( e_{1}^{\theta} \right)}^{T}}}};$updating the covariance matrix of noise: $\left\{ {\begin{matrix}{R_{1} = {H_{1}^{\theta} - {C_{1}^{\theta}{P_{1}^{\theta, -}\left( C_{1}^{\theta} \right)}^{T}}}} \\{Q_{1}^{\theta} = {K_{1}^{\theta}{H_{1}^{\theta}\left( K_{1}^{\theta} \right)}^{T}}}\end{matrix};} \right.$ correcting the state estimate: {circumflex over(θ)}⁻ _(l)={circumflex over (θ)}⁻ _(l)+K^(θ) _(l)e^(θ) _(l); updatingthe estimate error covariance of state: P^(θ,−) _(l)=(I−K^(θ) _(l)C^(θ)_(l))P^(θ,−) _(l), where C^(θ) _(l) is the Jacobian matrix of theobservation function of power system at the moment t_(1,0) applied inelectric vehicles, and${C_{1}^{\theta} = \left. \frac{\partial{G\left( {{\hat{x}}_{1,0},\theta,u_{1,0}} \right)}}{\partial\theta} \right|_{\theta = {\hat{x}}_{1}^{-}}};$cycling the operations of step 3 and step 4 until the moment t_(k,l),performing time update on the parameter observer AEKF_(θ) to get theprior estimate {circumflex over (θ)}⁻ _(k) of parameter θ at the momentt_(k,l), wherein $\left\{ {\begin{matrix}{{\hat{\theta}}_{k}^{-} = {\hat{\theta}}_{k - 1}} \\{P_{k}^{\theta, -} = {P_{k - 1}^{\theta} + Q_{k - 1}^{\theta}}}\end{matrix};} \right.$ performing time update on the state observerAEKF_(x) to get the prior estimate {circumflex over (x)}⁻ _(k-1,l) ofstate {circumflex over (x)}⁻ _(k-1,l) at the moment t_(k,l), wherein$\left\{ {\begin{matrix}{{\hat{x}}_{{k - 1},l}^{-} = {F\left( {{\hat{x}}_{{k - 1},{l - 1}}^{-},{\hat{\theta}}_{k}^{-},u_{{k - 1},{l - 1}}} \right)}} \\{P_{{k - 1},l}^{x, -} = {{A_{{k - 1},{l - 1}}P_{{k - 1},{l - 1}}^{x}A_{{k - 1},{l - 1}}^{T}} + Q_{{k - 1},{l - 1}}^{x}}}\end{matrix},} \right.$ A_(k-1,l-1) is the Jacobian matrix of the statefunction of power system at the moment t_(k,l) applied in electricvehicles, and${A_{{k - 1},{l - 1}} = \left. \frac{\partial{F\left( {x,{\hat{\theta}}_{k}^{-},u_{{k - 1},l}} \right)}}{\partial x} \right|_{x = {\hat{x}}_{{k - 1},{l - 1}}}};$updating the state observer AEKF_(x) based on the measurement to obtainthe posterior estimate {circumflex over (x)}⁻ _(k-1,l) of state x at themoment t_(k,l), updating the innovation matrix for state estimation toget: e_(k-1,l)=Y_(k-1,l)G({circumflex over (x)}⁻ _(k-1,l),{circumflexover (θ)}⁻ _(k),u_(k-1,l)), wherein the Kalman gain matrix isK ^(x) _(k-1,l) =P ^(x−) _(k-1,l)(C ^(x) _(k-1,l))^(T)(C ^(x) _(k-1,l) P^(x,−) _(k-1,l)(C ^(x) _(k-1,l))^(T) +R _(k-1,l-1))⁻¹; matching thecovariance adaptively:${H_{{k - 1},l}^{x} = {\frac{1}{M_{x}}{\sum\limits_{i = {l - M_{x} + 1}}^{l}\; {e_{{k - 1},}e_{{k - 1},l}^{T}}}}};$updating the noise covariance: $\left\{ {\begin{matrix}{R_{{k - 1},l} = {H_{{k - 1},l}^{x} - {C_{{k - 1},l}^{x}{P_{{k - 1},l}^{x, -}\left( C_{{k - 1},l}^{x} \right)}^{T}}}} \\{Q_{{k - 1},l}^{x} = {K_{{k - 1},l}^{x}{H_{{k - 1},l}^{x}\left( K_{{k - 1},l}^{x} \right)}^{T}}}\end{matrix};} \right.$ correcting the state estimate:{circumflex over (x)} ⁻ _(k-1,l) ={circumflex over (x)} ⁻ _(k-1,l) +K^(x) _(k-1,l) [Y _(k-1,l) −G({circumflex over (x)} ⁻_(k-1,l),{circumflex over (θ)}⁻ _(k) ,u _(k-1,l))]; updating the errorcovariance of state estimate;P ^(x,−) _(k-1,l)=(I−K ^(x) _(k-1,l) C ^(x) _(k-1,l))P ^(x,−) _(k-1,l),where C^(x) _(k-1,l) is the Jacobian matrix of the observation functionof power system at the moment t_(k,l) applied in electric vehicles, and${C_{{k - 1},l}^{x} = {\left. \frac{\partial{G\left( {x,{\hat{\theta}}_{k}^{-},u_{{k - 1},l}} \right)}}{\partial x} \middle| x \right. = {\hat{x}}_{{k - 1},l}}};$updating the parameter observer AEKF_(θ) based on the measurement toobtain the posterior estimate {circumflex over (θ)}⁻ _(k) of parameter θat the moment t_(k,θ,l); updating the innovation matrix for parameterestimation to get: e^(θ) _(k)=Y_(k,θ)−G({circumflex over (x)}⁻_(k,θ),{circumflex over (θ)}_(k),u_(k,θ)), wherein the Kalman gainmatrix is:K ^(x) _(k-1,l) =P ^(x,−) _(k-1,l)(C ^(x) _(k-1,l))^(T)(C ^(x) _(k-1,l)P ^(x,−) _(k-1,l)(C ^(x) _(k-1,l))^(T)+R_(k-1,l-1))⁻¹; matching thecovariance adaptively:${H_{k}^{\theta} = {\frac{1}{M_{\theta}}{\sum\limits_{i = {1 - M_{\theta} + 1}}^{l}\; {e_{k}^{\theta}\left( e_{k}^{\theta} \right)}^{T}}}};$updating the noise covariance: $\quad\left\{ {\begin{matrix}{R_{k} = {H_{k}^{\theta} - {C_{k}^{\theta}{P_{k}^{\theta, -}\left( C_{k}^{\theta} \right)}^{T}}}} \\{Q_{k}^{\theta} = {K_{k}^{\theta}{H_{k}^{\theta}\left( K_{k}^{\theta} \right)}^{T}}}\end{matrix};} \right.$ correcting the state estimate: {circumflex over(θ)}⁺ _(k)={circumflex over (θ)}⁻ _(k)+K⁰ _(k)e⁰ _(k); updating theerror covariance of state estimate: P^(0,+) _(k)=(I−K⁰ _(k)C⁰_(k))P^(θ,−) _(k) where C⁰ _(k) is the Jacobian matrix of theobservation function of power system at the moment t_(k,0−L) applied inelectric vehicles, and${C_{k}^{\theta} = \left. \frac{\partial{G\left( {{{\hat{x}}_{k,0}\theta},u_{k,\theta}} \right)}}{\partial\theta} \right|_{\theta = {\hat{x}}_{1}^{-}}};$and cycling the above operations until the estimation is completed. 2.The method according to claim 1, wherein when performing time update onthe state observer AEKF_(x), the cycle of the microscopic time scale isl=1:L; when l=L, the macroscopic time scale transfers to k from k-1, andthe microscopic time scale transfers to L from
 0. 3. The methodaccording to claim 1, wherein the cycle data of the power system of theelectric vehicle is input in a state estimation filter in real time. 4.The method according to claim 2, wherein the cycle data of the powersystem of the electric vehicle is input in a state estimation filter inreal time.
 5. A power battery management system applying the methodaccording to claim
 1. 6. A power battery management system applying themethod according to claim
 2. 7. A power battery management systemapplying the method according to claim
 3. 8. A power battery managementsystem applying the method according to claim 4.